Toys

As you are reading this you will realize it is not complete, as I am not finishing this at once and will add to it every so often. Note: this is only for regular 3x3 rubiks cube. Not Sudocube, special patterned ones, or different dimensions of cubes however this is good help for other sizes of cubes.

The first thing you must realize is how a rubik's cube works. There are 26 cubies that seem to turn. however it is important to know that the centre cubes never move. They are fixed. These are called centre pieces, and there are 6. Yes, they turn around an axis but never move.Upon examination you will realize that not all cubes are the same. There are also corner pieces, which there are 8 of. Each of them have three stickers on them and are a part of two separate faces. Then there are edge pieces, of which you will find 12, which have two stickers on each. I recommend taking apart your cube, examining how it works. To do this, simply turn one face (a side, with 9 cubes) 45 degrees. Then, with your finger, pry up one of the edgepieces that was moved. Continue from there. Pull the rest apart. Putting it back together isn`t very hard, just remember to put it in the solved position. This is because chances are when you don`t, 12-1 odds are it can`t be solved, because there are some permutations (positions) that are normally impossible. (as a side note, don`t complain how hard it is to put back together because the 4x4, 5x5, and on, are much harder).

Do not skip reading that. It is important. This is also important or you will not understand the rest of this. Heres another term: an algorithm is a set of moves. You might say, aaaaah, so if I learn this magical algorithm, I can solve the cube? Well, not quite. You see, there are over 43 quintillion permutations of the cube (43,000,000,000,000,000,000+). Right? So one set of moves cannot solve it. Instead, there are several steps that orient (place each cube in the right place) and permute (solve the cubes completely so they are in there spot facing the right way in relation to the others). But there are many algorithms that vary slightly in each step depending on the permutation of the cube. So as I walk you through these steps and algorithms, you are going to need to know the following things. To simplify the algorithmns, here are the letters that will stand for each face: U (up face, on top); D (down, bottom); F (front, so facing you); B (back); L (left); and R (you guessed it! Right). So just so you know, that is U, D, F, B, L, R. Don`t ask which goes with which colour because none do. It is just how you are holding it at one time. Now you need to know the different types of turns: the quarter turn and the half turn. The quarter turn is a turn of a face one quarter of the way around clockwise, or 90 degrees. Then of course a half turn is a turn of a face halfway around axis (180 degrees, and it doesn't matter which way you turn it. However, if you want to get very fast, this is something you should think about). There is no need for a three-quarter turn because it can be shown and done as a backward quarter turn, and of course a full turn is not a move at all. In algorithms, a quarter turn is represented by just the letter of the face. So F alone means turning the front face clockwise a quarter turn (90 degrees). Or for example FRU means turning the front face a quarter turn, then the same for the right face and up face - but note: it MUST be done in the order it is in the algorithm or it will never work. A half turn is notated the same exept there is a 2 after the letter. So F2 means turn the front face a half turn (or two quarter turns). All that's left now is the counterclockwise quarter turn, which is indicated with an apostrophe after the letter. So F' means turn the front face counterclockwise a quarter turn. That is all the notation you will need to know for now, and for these instructions. Well that 's enough of that. Yes, yes, how to solve a 3 by 3.

STEP 1: The first layer.

DO NOT skip to here. There are no algorithms for this layer. It is intuitive (you learn it by doing it). However, you still need to read the above paragraphs, as it may help you. By the first layer, that means completely solving the U face (the top 9 cubes). Most cubers start with the same face every time and its usually the white face. But irregardless of what you chose, the procedure is the same. You must first make the cross on the top. This means that the four edge pieces are solved on the first layer (and of course are on the same side as their corresponding centre piece). How to do this however is hard to explain, as it is intuitive.

go to the following page:

http://www.corpusvile.com/docs/rubikscube/1.jpg).

This is what you are aiming for. The cross is formed, but I want you to try and find the mistake in the picture.

No, no it isn't because the rest of the stickers were removed. If you look at your cube, solved or not, you will see that this cube is messed up because the white, blue and red centre pieces are in the worng places. Blue and red appear to have been switched. This is something you are going to need to remember, the order of the colours. With white on top (and of course yellow on the bottom), the colours are, starting at blue moving left: blue, red, green, orange. This may seem obvious but it is a good thing to remember, especially if you want to learn to solve a cube that is even, like 2x2, 4x4, etc.

There are 8 corner pieces with 3 orientations each, 12 edge pieces with 2 orientations each, giving a maximum of 8!·12!·38·212 positions. This limit is not reached because:

• The total twist of the cubes is fixed (3)
• The total number of edge flips is even (2)
• The pieces have an even permutation (2)

This leaves 8!·12!·37·210 = 43,252,003,274,489,856,000 or 4.3·1019 positions.

Total Positions

There are exactly 43,252,003,274,489,856,000 permutations, which is approximately forty-three quintillion. The puzzle is often advertised as having only "billions" of positions, as the larger numbers could be regarded as incomprehensible to many. To put this into perspective, if every permutation of a 57mm Rubik's Cube were lined up end to end, it would stretch out approximately 261 light-years.

(see related link)